TY - JOUR
T1 - New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications
AU - Gu , Dong-Qin
AU - Wang , Zhong-Qing
AU - Zhang , Chao
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 453
EP - 488
PY - 2023
DA - 2023/04
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2022-0109
UR - https://global-sci.org/intro/article_detail/nmtma/21585.html
KW - Rational collocation methods, Birkhoff interpolation, fast and stable algorithms.
AB - <p style="text-align: justify;">Based on the rational system of Legendre rational functions, we construct
two set of new interpolation basis functions on the unbounded intervals. Their explicit expressions are derived, and fast and stable algorithms are provided for computing the new basis functions. As applications, new rational collocation methods
based on these new basis functions are proposed for solving various second-order
differential equations on the unbounded domains. Numerical experiments illustrate
that our new methods are more effective and stable than the existing collocation
methods.</p>